Imagine 2 situations: driving down a hill with no power and driving up a hill with maximum power. There are very different power figures being transferred from the engine to the wheels in those two situations and it’s the same when you start braking.
If you suddenly start going uphill, your driveshaft or differential won’t break under the increased stress, nor will it do that if you start braking.
From the point of a car internals like diff and shaft that you ask, it makes no difference if you brake or if you drive a very steep incline. Braking is just another force that’s slowing the wheels. The only situation where it could be dangerous is if you would suddenly drop the clutch in manual while holding brakes. In normal situation that would break the traction
The engine outputs torque to the drive train. Brakes are stronger than the engine so they overcome its force and make it slow down.
In an automatic you have a torque converter. It’s a fluid coupling between the engine and the drive train. The engine spins a propeller, and the drive train is connected to an impeller. It allows the engine to transmit torque to the drive train, but still keep spinning even when the drive train comes to a complete stop. This is why autos creep forward when you get off the brakes.
In a manual you have the clutch. It’s a physical coupling but you can manually disconnect it with a pedal if you want to come to a stop.
Newer automatics often have a clutch or some kind of fancy system of clutches. They’re physical connections, but they’re controlled electronically instead of manually. (These also creep forward, but only because they’re programmed to do so since drivers prefer it)
In a manual if you come to a stop without disengaging the clutch the engine stalls. This will happen long before anything in the drivetrain breaks. It’s probably not great for the engine, but it won’t break it.
No? Unless you’re hitting both the accelerator and brakes at the same time and I don’t know why you’d do that.
If you take your foot off the gas there’s no active power being delivered the system and the braking the wheels will in turn slow down the driveshaft and differential as well.
You’d only have issues if you have competing forces e.g., braking the vehicle while also mashing the accelerator.
Latest Answers